You'd need either a digit for 100, or some notation for grouping digits.E.g.:

2^10 => A2^11 => B2^12 => C...

but since we can't realistically have an infinite number of unique symbols,a grouping notation might be better:

2^100 + 2^50 + 2^10 + 2^2 = (100)(50)(10)2

> Every positive integer is a sum of non-negative powers of two.> No integer other than two has that property.

I believe you are missing the word "unique" in that sentence. If you allowrepeated powers, one can do this:

17 = 3^2 + 3^1 + 3^1 + 3^0 + 3^0 = "21100" to "base 3".

> We could write 1/2 = -1> 1/4 = -2; 1/8 = -3; 1/16 = -4; 0 = -oo> > 3/4 = -1 -2> 1/3 = -2 -4 ...; an infinite series.> > Let's try adding.> 21 + 31 = 3211 = 322 = 33 = 4. Check. 6 + 10 = 16.> > 210 + 210 = 221100 = 321> 2 * abcd = a+1 b+1 c+1 d+1> > Looks like fun. If you can't remember the details, let's reinvent them.> >> and so forth. Obviously there is no way of writing zero, and the order of>> the digits is arbitrary: I could have written either "12" or "21" for>> decimal 6.>>>> Unfortunately I have forgotten all details about this except the basic>> notation, including the name of the book.>>>> Is there a name for this notation, is it useful for anything, and where>> might I find out more about it?